Context: Large surveys such as the Sloan Digital Sky Survey have made large amounts of spectroscopic and photometric data of galaxies available, thereby providing important information for studying galaxy evolution in dense environments. Aims: We have selected a sample of 88 nearby (z < 0.1) galaxy clusters from the SDSS-DR4 with redshift information for the cluster members. In particular, we focus on the galaxy morphological distribution, the velocity dispersion profiles, and the fraction of blue galaxies in clusters. Methods: Cluster membership was determined using the available velocity information. We derived global properties for each cluster, such as their mean recessional velocity, velocity dispersion, and virial radii. Cluster galaxies were grouped into two families according to their u-r colours. Results: The total sample consists of 10 865 galaxies. As expected, the highest fraction of galaxies (62%) turned out to be early-type (red) ones, located at smaller distances from the cluster centre and showing lower velocity dispersions than late-type (blue) ones. The brightest cluster galaxies are located in the innermost regions and show the smallest velocity dispersions. Early-type galaxies also show constant velocity dispersion profiles inside the virial radius and a mild decline in the outermost regions. In contrast, late-type galaxies show ever decreasing velocity dispersions profiles. No correlation has been found between the fraction of blue galaxies and cluster global properties,such as cluster velocity dispersion or galaxy concentration. In contrast, we find a correlation between the X-ray luminosity and the fraction of blue galaxies. Conclusions: These results indicate that early- and late-type galaxies may have had different evolutions. Thus, blue galaxies are located in more anisotropic and radial orbits than early-type ones. Their star formation seems to be independent of the cluster global properties in low-mass clusters, but not for the most massive ones. We consider that it is unlikely that the whole blue population consists of recent arrivals to the cluster. These observational results suggest that the global environment could be important for driving the evolution of galaxies in the most massive cluster (σ > 800 km s-1). However, the local environment could play a key role in the galaxy evolution for low-mass clusters. Table 1 is only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/471/17